Export of sinking particles from the surface ocean is critical for carbon sequestration and for providing energy to the deep-ocean biosphere. The magnitude and spatial patterns of this flux have been estimated in the past by satellite-based algorithms and ocean biogeochemical models; however, these estimates remain uncertain. Here, we present a novel analysis of a global compilation of \textit{in situ} ocean particle size spectra from Underwater Vision Profiler 5 (UVP5) measurements, from which we determine particulate carbon fluxes. Using a machine learning algorithm, we extrapolate sparse observations of particle abundance by size to the global ocean from oceanographic variables that are more commonly observed. We reconstruct global maps of particle size distribution parameters for large sinking particles (80 \textmu{}m to 2.6 cm), and combine them with empirical relationships to calculate the sinking carbon flux from the euphotic zone and the wintertime mixed layer depth. Our flux reconstructions are comparable to other estimates, but suggest a less variable seasonal cycle in the tropical ocean, and a more continuous export in the Southern Ocean than previously thought. Because our estimates are not bounded by a specific depth horizon, we reconstruct export at multiple depths, and find that export from the wintertime mixed layer globally exceeds that from the euphotic zone. Our estimates provide a baseline for more accurate understanding of particle cycles in the ocean, and open the way to fully three-dimensional global reconstructions of particle size spectra and fluxes in the ocean, supported by the growing database of UVP5 observations.